Attending: Chris Harrow, Dennis Wilson, Lynnae Boudreau, Mike Sanders, Leah Kilgore, Kathy Butts
Dennis gave several examples of lessons he's used in class:
1. Graphed equations, created tangents as a point travels, constructed point with the slope as the y-value, then constructed a locus of that point. Track with changes to original function. Can repeat procedure to generate second derivative
2. NSPire to create 3-D washers and slices for volumes.
3. CAS to use locus to graph inverse functions.
4. Creating conics (use CAS, and Geogebra): parabola
5. Bending directrices
Chris gave a few examples as well:
1. Polar graphing: rose graphs
2. Description of conic CAS program, with sliders.
3. Bending asymptotes for rational functions.
We considered a number of ways to modify and track changes in functions:
2. Relate what happens when leading coefficients/multipliers for trig functions are other functions rather than real numbers.
3. Relate trig function on a cartesian plane-- with center, floor, and ceiling lines-- to trig functions on a polar graph with center, floor, and ceiling circles.
We plan to continue meeting next school year, with the same general plan.
February 3, 2011:
Attending: Lynnae Boudreau, Kathy, Butts, Chris Harrow, Leah Kilgore, Randy Murphy, Mike Sanders, Dennis Wilson
I. Round-the-room discussion of technology, some CAS-specific and some more general:
Discussed i-pad vs. CAS: touch screen is easy to operate, CAS is complicated, with a steep learning
curve coming off of 84’s. If starting with NSpire, not the same learning curve as moving from 84.
Wolfram-Alpha (W-A), PocketCAS app for i-pad—do they have split-screen capability? Dennis has AP Cal use
W-A regularly—“fair game” on homework.
VNC (Virtual Network Computing) (Mac and PC) app for wireless networking. VNC Viewer to see what all laptops
in a classroom are doing.
Limitation with i-pad is projection—has to be written into the app—so is printing; classroom navigating would be
critical.
Standardized testing is an issue for i-pad—without approval for SAT’s, we would continue to be dual platform with handhelds; understand Internet connection issues during testing.
At Westminster in the beginning of CAS use, 2-3 year transition from 84’s to NSpire, then everyone got NSpire as junior. Now, everyone in US uses CAS.
Georgia looking at i-pads for on-line textbooks. Georgia also looking at doing away with IMP, to let districts decide.
Viewed TED talk by Conrad Wolfram—led to long conversation about use of technology and changing math pedagogy. What to teach and how? Idea that we should teach from the beginning with computers—to reduce the emphasis on computation—intriguing.
II. CAS How-to:
Looked briefly at on-line activities available on TI web site.
III. Next meeting: Thursday, April 14th, 5PM, Lovett
Dennis will present his related rates bicycle lesson (with locus).
Chris will present his eccentric conics lesson.
Call for lessons to develop for next time
November 11, 2010:
We briefly shared CAS experiences since the last meeting.
Chris gave us a lesson on creating and using sliders directly on handhelds—useful for any type of function, and can be used for a wide variety of student play and exploration.
Included in the lesson was a demonstration of multiple graphing from a single function line using brackets.
We moved from there to linear regression, as well as a number of other topics:
“linearizing” exponential data
using sliders to estimate a line of best fit
adding movable lines to scatterplots
constructing residuals with perpendicular lines
finding the “centroid” of a set of data by finding all 0-sum residuals
using that centroid with point-slope and the square of residuals to find the line of best fit (demo for students)
We started with introductions over pizza, and shared our experience levels with CAS. Those levels range from CAS experimenters to deep CAS users.
We discussed ways to incorporate CAS into classrooms, even if students don't have individual handhelds. This includes using on-line CAS utilities like Wolfram Alpha and Geogebra.
Chris gave us a lesson on building and using sliders to enable students to explore the effects of a, b, and c in a quadratic equation on a quadratic graph.
This led to a more general conversation about conics.
April 14, 2011
Attending: Chris Harrow, Dennis Wilson, Lynnae Boudreau, Mike Sanders, Leah Kilgore, Kathy Butts
Dennis gave several examples of lessons he's used in class:
1. Graphed equations, created tangents as a point travels, constructed point with the slope as the y-value, then constructed a locus of that point. Track with changes to original function. Can repeat procedure to generate second derivative
2. NSPire to create 3-D washers and slices for volumes.
3. CAS to use locus to graph inverse functions.
4. Creating conics (use CAS, and Geogebra): parabola
5. Bending directrices
Chris gave a few examples as well:
1. Polar graphing: rose graphs
2. Description of conic CAS program, with sliders.
3. Bending asymptotes for rational functions.
We considered a number of ways to modify and track changes in functions:
1. Square, square root, absolute value, reciprocal transformations
2. Relate what happens when leading coefficients/multipliers for trig functions are other functions rather than real numbers.
3. Relate trig function on a cartesian plane-- with center, floor, and ceiling lines-- to trig functions on a polar graph with center, floor, and ceiling circles.
We plan to continue meeting next school year, with the same general plan.
February 3, 2011:
Attending: Lynnae Boudreau, Kathy, Butts, Chris Harrow, Leah Kilgore, Randy Murphy, Mike Sanders, Dennis Wilson
I. Round-the-room discussion of technology, some CAS-specific and some more general:
Discussed i-pad vs. CAS: touch screen is easy to operate, CAS is complicated, with a steep learning
curve coming off of 84’s. If starting with NSpire, not the same learning curve as moving from 84.
Wolfram-Alpha (W-A), PocketCAS app for i-pad—do they have split-screen capability? Dennis has AP Cal use
W-A regularly—“fair game” on homework.
VNC (Virtual Network Computing) (Mac and PC) app for wireless networking. VNC Viewer to see what all laptops
in a classroom are doing.
Limitation with i-pad is projection—has to be written into the app—so is printing; classroom navigating would be
critical.
Standardized testing is an issue for i-pad—without approval for SAT’s, we would continue to be dual platform with handhelds; understand Internet connection issues during testing.
At Westminster in the beginning of CAS use, 2-3 year transition from 84’s to NSpire, then everyone got NSpire as junior. Now, everyone in US uses CAS.
Georgia looking at i-pads for on-line textbooks. Georgia also looking at doing away with IMP, to let districts decide.
Viewed TED talk by Conrad Wolfram—led to long conversation about use of technology and changing math pedagogy. What to teach and how? Idea that we should teach from the beginning with computers—to reduce the emphasis on computation—intriguing.
II. CAS How-to:
Looked briefly at on-line activities available on TI web site.
III. Next meeting: Thursday, April 14th, 5PM, Lovett
Dennis will present his related rates bicycle lesson (with locus).
Chris will present his eccentric conics lesson.
Call for lessons to develop for next time
November 11, 2010:
We briefly shared CAS experiences since the last meeting.
Chris gave us a lesson on creating and using sliders directly on handhelds—useful for any type of function, and can be used for a wide variety of student play and exploration.
Included in the lesson was a demonstration of multiple graphing from a single function line using brackets.
We moved from there to linear regression, as well as a number of other topics:
“linearizing” exponential data
using sliders to estimate a line of best fit
adding movable lines to scatterplots
constructing residuals with perpendicular lines
finding the “centroid” of a set of data by finding all 0-sum residuals
using that centroid with point-slope and the square of residuals to find the line of best fit (demo for students)
Chris posted a lesson for linear regression development to the wiki.
Dennis mentioned something about using locus,which will be a lesson next time.
September 29, 2010:
We started with introductions over pizza, and shared our experience levels with CAS. Those levels range from CAS experimenters to deep CAS users.
We discussed ways to incorporate CAS into classrooms, even if students don't have individual handhelds. This includes using on-line CAS utilities like Wolfram Alpha and Geogebra.
Chris gave us a lesson on building and using sliders to enable students to explore the effects of a, b, and c in a quadratic equation on a quadratic graph.
This led to a more general conversation about conics.